Heat engines & refrigerators worksheet with answers

Free printable Heat engines & refrigerators worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 42%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 600 MWη = 42%
Q̇H = MW
2.Easy
houseoutside airHPQ̇H​ = 18 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 5 delivers 18 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 5Q̇H = 18 kW
Q̇L = kW
3.Medium
TH​ = 650 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 650 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 35 °CTL​ = 4 °CRQ̇H​ = ?Q̇L​ = 5 kWẆ

A reversible refrigerator keeps a cold room at 4 °C by removing 5 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = 4 °CTH = 35 °CQ̇L = 5 kW
Q̇H = kW
5.Hard
TH​ = 950 °CT0​ = 20 °CTL​ = -5 °CERWQ̇H​ = 100 kWQ̇L​ = ?

A Carnot heat engine receives 100 kW of heat from a source at 950 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -5 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 950 °CT0 = 20 °CTL = -5 °CQ̇H = 100 kW
Q̇L = kW
6.Hard
TH​ = 20 °CTL​ = 7 °CHPQ̇H​ = 9 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 7 °C outside, delivering 9 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 7 °CQ̇H = 9 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 1429 MW
  2. 2. Q̇L = 14.4 kW
  3. 3. ηmax = 66.08 %
  4. 4. Q̇H = 5.559 kW
  5. 5. Q̇L = 815.5 kW
  6. 6. Ẇmin = 0.3991 kW

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